Details

analyze428.0ms (7.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	46
1	34	46
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample29.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	194×	body	128	valid
4.0ms	16×	body	4096	valid
4.0ms	17×	body	2048	valid
2.0ms	12×	body	1024	valid
1.0ms	9×	body	512	valid
1.0ms	8×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

36.6b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.2b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.8b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
27.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`pow1_binary64_2185` `add-log-exp_binary64_2163`
7×	`*-un-lft-identity_binary64_2124`
6×	`add-sqr-sqrt_binary64_2146`
5×	`add-cube-cbrt_binary64_2159`
4×	`sqrt-prod_binary64_2140` `sqrt-div_binary64_2141` `flip3-+_binary64_2127` `flip-+_binary64_2098` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`sqrt-pow1_binary64_2142`
2×	`sum-log_binary64_2215` `+-commutative_binary64_2054` `pow1/2_binary64_2204` `associate-*r/_binary64_2066`
1×	`pow-prod-down_binary64_2195` `distribute-lft-out_binary64_2075` `rem-sqrt-square_binary64_2137`

Counts

4 → 51

Calls

4 calls:

12.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
7.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

series185.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
27.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
24.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
23.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify79.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4937	1040
1	4937	1040

prune81.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	6	64

Error

14.7b

Counts

64 → 6

Compiler

Compiled 1322 to 603 computations (54.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
7.2b	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
27.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite63.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`sqrt-prod_binary64_2140`
58×	`add-sqr-sqrt_binary64_2146`
34×	`sqrt-pow1_binary64_2142`
29×	`pow1_binary64_2185`
28×	`sqrt-div_binary64_2141`
18×	`add-cube-cbrt_binary64_2159` `pow1/2_binary64_2204` `*-un-lft-identity_binary64_2124`
15×	`swap-sqr_binary64_2091`
10×	`rem-sqrt-square_binary64_2137`
9×	`unswap-sqr_binary64_2092` `pow-prod-up_binary64_2194` `associate-l_binary64_2065` `flip3-+_binary64_2127` `associate-r_binary64_2064` `flip-+_binary64_2098`
6×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`pow-prod-down_binary64_2195` `pow-sqr_binary64_2097`
4×	`sqr-abs_binary64_2139` `frac-times_binary64_2134`
2×	`associate-l/_binary64_2067` `associate-r/_binary64_2066`
1×	`sqrt-unprod_binary64_2144` `sum-log_binary64_2215` `*-commutative_binary64_2055` `prod-exp_binary64_2173` `pow-plus_binary64_2187` `+-commutative_binary64_2054` `rem-square-sqrt_binary64_2136` `pow2_binary64_2205` `cbrt-unprod_binary64_2157`

Counts

4 → 128

Calls

4 calls:

19.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
18.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series101.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
26.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
23.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
22.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify63.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5171	2274

prune140.0ms (2.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	140	6	146

Error

14.7b

Counts

146 → 6

Compiler

Compiled 3687 to 1278 computations (65.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
0.4b	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
27.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.6b	(sqrt.f64 (.f64 (.f64 im im) 2))

rewrite44.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64_2146`
50×	`sqrt-prod_binary64_2140`
38×	`*-un-lft-identity_binary64_2124`
36×	`times-frac_binary64_2130`
26×	`add-cube-cbrt_binary64_2159`
12×	`difference-of-squares_binary64_2093`
11×	`pow1_binary64_2185`
9×	`associate-/r*_binary64_2068`
6×	`distribute-lft-out--_binary64_2076` `add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
4×	`sqrt-pow1_binary64_2142` `associate-/l*_binary64_2069` `sqrt-div_binary64_2141`
3×	`pow-prod-down_binary64_2195` `cancel-sign-sub-inv_binary64_2090`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/r/_binary64_2070` `pow1/2_binary64_2204`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `sqrt-undiv_binary64_2145` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `sub-neg_binary64_2117` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 108

Calls

4 calls:

15.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series172.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

92.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
30.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
27.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))
22.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify73.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5054	3621

prune150.0ms (2.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	115	5	120
Fresh	1	3	4
Picked	1	0	1
Done	1	0	1
Total	118	8	126

Error

9.5b

Counts

126 → 8

Compiler

Compiled 3685 to 1338 computations (63.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
0.3b	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
0.4b	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
27.2b	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

rewrite82.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`sqrt-prod_binary64_2140`
143×	`add-sqr-sqrt_binary64_2146`
112×	`times-frac_binary64_2130`
100×	`*-un-lft-identity_binary64_2124`
72×	`add-cube-cbrt_binary64_2159`
60×	`associate-r_binary64_2064`
28×	`difference-of-squares_binary64_2093`
14×	`distribute-lft-out--_binary64_2076`
11×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
9×	`associate-/r*_binary64_2068`
7×	`pow1_binary64_2185`
6×	`associate-/l*_binary64_2069` `sqrt-div_binary64_2141` `add-log-exp_binary64_2163`
5×	`unswap-sqr_binary64_2092`
4×	`associate-/r/_binary64_2070`
3×	`flip--_binary64_2099` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090` `associate-l_binary64_2065`
2×	`cbrt-undiv_binary64_2158` `prod-exp_binary64_2173` `div-inv_binary64_2121` `div-exp_binary64_2175` `cbrt-unprod_binary64_2157`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `-commutative_binary64_2055` `sqrt-undiv_binary64_2145` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `associate-r/_binary64_2066` `flip3-+_binary64_2127` `flip-+_binary64_2098` `frac-2neg_binary64_2135`

Counts

4 → 198

Calls

4 calls:

30.0ms	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
13.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

series243.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

105.0ms	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
88.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
27.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
23.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

simplify84.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4959	6419
1	4959	6419

prune247.0ms (4.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	203	7	210
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	206	12	218

Error

3.0b

Counts

218 → 12

Compiler

Compiled 6488 to 2249 computations (65.3% saved)

regimes1.2s (22.1%)

Accuracy

Total 16.4b remaining (87.9%)

Threshold costs 0b (0%)

Compiler

Compiled 9395 to 6300 computations (32.9% saved)

bsearch84.0ms (1.5%)

Steps

Iters	Range	Point
9	1.7431414725320761e+62	6.669349745869486e+68	2.0982341812511796e+68
9	6.221096012041714e-309	8.608594865326139e-302	6.71142159152561e-309
8	-2.478048149990556e+141	-1.6723254658902209e+137	-2.4368798138824472e+141

Iters

Range

Point

1.7431414725320761e+62

6.669349745869486e+68

2.0982341812511796e+68

6.221096012041714e-309

8.608594865326139e-302

6.71142159152561e-309

-2.478048149990556e+141

-1.6723254658902209e+137

-2.4368798138824472e+141

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	101
1	61	101

end0.0ms (0%)

sample1.9s (34.1%)

Algorithm

1×

intervals

Results

292.0ms	6084×	body	128	valid
149.0ms	522×	body	4096	valid
145.0ms	624×	body	2048	valid
73.0ms	412×	body	1024	valid
29.0ms	223×	body	512	valid
14.0ms	135×	body	256	valid

Compiler

Compiled 1321 to 880 computations (33.4% saved)

Details

analyze428.0ms (7.7%)

sample29.0ms (0.5%)

simplify7.0ms (0.1%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite32.0ms (0.6%)

series185.0ms (3.3%)

simplify79.0ms (1.4%)

prune81.0ms (1.5%)

localize12.0ms (0.2%)

rewrite63.0ms (1.1%)

series101.0ms (1.8%)

simplify63.0ms (1.1%)

prune140.0ms (2.5%)

localize12.0ms (0.2%)

rewrite44.0ms (0.8%)

series172.0ms (3.1%)

simplify73.0ms (1.3%)

prune150.0ms (2.7%)

localize13.0ms (0.2%)

rewrite82.0ms (1.5%)

series243.0ms (4.4%)

simplify84.0ms (1.5%)

prune247.0ms (4.4%)

regimes1.2s (22.1%)

bsearch84.0ms (1.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.9s (34.1%)

Profiling